SOLUTION: If Rita is eight years old, is twice as old as her sister. How old will Rita be when she is one and a four times as old as her sister? I tried solving this problem but I don'

Question 218792: If Rita is eight years old, is twice as old as her sister. How old will Rita be when she is one and a four times as old as her sister?

I tried solving this problem but I don't get the concept.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
This is a ratio problem
Let = Rita's age
Let = Sister's age
The thing to notice here, is that with any 2 people,
the difference in their ages will always be the same,
but one will only be twice the other's age at one time
in their lives.
Say I'm 20 and you're 10. In one year the ratio is
, no longer
------------------------------------------------------
The difference in Rita's and her Sister's ages (always) is
or,

So, I can state that

Multiply both sides by

(since )
Rita will be 20 when she is times as old as her sister

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
If Rita is eight years old, is twice as old as her sister. How old will Rita be when she is one and a four times as old as her sister?

Let the amount of years that it takes for Rita to be 1 1/4, or times her sister's age be y

Since Rita is 8, and her sister's 4

We'll therefore have:

32 + 4y = 20 + 5y ----- Cross-multiplying

4y - 5y = 20 - 32

- y = - 12

y = = 12

Therefore, in 12 years' time, Rita will be times her sister's age, which means that she will be (8 + 12) years-old.

This would also mean that in 12 years' time, her sister will be 16 (4 + 12).

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Check
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20 = 20 (TRUE)
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